"We do need to have an inquiry, possibly inquiries, into what has happened," he said. "We are no longer talking here about politicians and celebrities, we are talking about murder victims, potentially terrorist victims, having their phones hacked into.

"It is absolutely disgusting, what has taken place, and I think everyone in this House [of Commons] and indeed this country will be revolted by what they have heard and what they have seen on their television screens."

Cameron stated that "vital areas" including why the original police inquiry failed "to get to the bottom of what happened" must be examined.

However, Labor leader Ed Miliband criticized Cameron for being "out of touch", when it was explained that an inquiry could not be launched until the ongoing police investigation had concluded. Miliband insisted that it was "possible for the prime minister to start the process now".

"It may be possible to make a start on other elements," Cameron conceded, adding that he would be willing to hold talks with Miliband and the other party leaders, Attorney General Dominic Grieve and Cabinet Secretary Sir Gus O'Donnell.

As well as calling on Cameron to back his calls for News International chief executive Rebekah Brooks - who was editor of the News of the World during the alleged Dowler hacking - to quit her position, Miliband also questioned the PM's decision to hire another former editor Andy Coulson as his communications director. Coulson quit the role earlier this year.

"He's got to accept that he made a catastrophic error of judgement by bringing Andy Coulson into the heart of the Downing Street machine," Miliband declared.

News International has said that it welcomes the proposal of a public inquiry into standards within the media, according to BBC News.